The density of rational points on non-singular hypersurfaces, II

• Autores: T. D. Browning, D.R. Heath-Brown, J.M. Starr
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 2, 2006, págs. 273-303
• Idioma: inglés
• DOI: 10.1112/s0024611506015784
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• Resumen

  • For any integers $d,n \geq 2$, let $X \subset \mathbb{P}^{n}$ be a non-singular hypersurface of degree $d$ that is defined over the rational numbers. The main result in this paper is a proof that the number of rational points on $X$ which have height at most $B$ is $O(B^{n - 1 + \varepsilon})$, for any $\varepsilon > 0$. The implied constant in this estimate depends at most upon $d$, $\varepsilon$ and $n$.